Superconvexity of the heat kernel on hyperbolic space with applications to mean curvature flow

Zhang, Yongzhe

doi:10.1090/proc/15379

Superconvexity of the heat kernel on hyperbolic space with applications to mean curvature flow
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Proc. Amer. Math. Soc. 149 (2021), 2161-2166 Request permission

Abstract:

We prove a conjecture of Bernstein that the heat kernel on hyperbolic space of any dimension is supercovex in a suitable coordinate and, hence, there is an analog of Huisken’s monotonicity formula for mean curvature flow in hyperbolic space of all dimensions.

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